$12.$ While you are waiting to check in$,$ an expert in statistics arrives at the hotel $($there is a conference on Statistics at the hotel that week$)$ and joins the check$-$in line. You establish a conversation with the expert and, after talking about the weather and the plans for the day, you engage in a discussion about the wait in the check$-$in line. The expert congratulates you for your observations regarding the arrival and service processes, but quickly observes that the service time actually follows an exponential distribution. The average processing rate is indeed of $10$ guests per hour. What is now the average amount of time $($in minutes$)$ that guests spend waiting and being served?